Abstract
In this note we consider the convergence near turning points of a class of finite difference schemes for a one-parameter family of semilinear elliptic systems
where λ ∈ ℝ, Ω is a bounded region in ℝn with boundary Γ∈ C 2,α, O < α < 1, and f ∈ C1,O (ℝ× × ℝm,ℝm).
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Böhmer, K.: Asymptotic expansion for the discretization error in linear elliptic boundary value problems on ge-neral regions. Math. Z. 177, 235–255 (1981)
Brezzi, F.; Rappaz, J.; Raviart, P.A.: Finite dimensional approximation of nonlinear problems. Part II: Limit points. Numer. Math. 37, 1–28 (1981)
Moore, G.; Spence, A.: The convergence of operator approximations at turning points. IMA J. Num. Anal. 1, 23–38 (1981)
Munz, H.: Uniform expansions for a class of finite difference schemes for elliptic boundary value problems. Math. Comp. 36, 155–170 (1981)
Munz, H.: Asymptotisches Verhalten des Fehlers eines Differenzenverfahrens für semilineare Systeme partieller Differentialgleichungen. Dissertation, Universität Tübingen, 1983
Pereyra, V.; Proskurowski, W.; Widlund, 0.: High order fast Laplace solvers for the Dirichlet problem on general re-gions. Math. Comp. 31, 1–16 (1977)
Starius, G.: Asymptotic expansions for a class of finite dif-ference schemes. Math. Comp. 37, 321. 326 (1981)
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© 1984 Springer Basel AG
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Munz, H. (1984). Asymptotic Error Expansion for Finite Difference Schemes for Elliptic Systems Near Turning Points. In: Küpper, T., Mittelmann, H.D., Weber, H. (eds) Numerical Methods for Bifurcation Problems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 70. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6256-1_24
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DOI: https://doi.org/10.1007/978-3-0348-6256-1_24
Publisher Name: Birkhäuser, Basel
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Online ISBN: 978-3-0348-6256-1
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